We discuss the relation between (topological) transitivity and strong transitivity of dynamical systems. We show that a transitive and open self-map of a compact metric space satisfying a certain expanding condition is strongly transitive. We also prove a couple of results for interval maps; for example it is shown that a transitive piecewise monotone interval map is strongly transitive.

In a recent paper by Monteiro and Svaiter, a hybrid proximal extragradient (HPE) framework was used to study the iteration-complexity of a first-order (or, in the context of optimization, second-order) method for solving monotone nonlinear equations. The purpose of this paper is to extend this analysis to study a prox-type first-order method for monotone smooth variational inequalities and incl...

Equilibrium problems have many uses in optimization theory and convex analysis and which is why different methods are presented for solving equilibrium problems in different spaces, such as Hilbert spaces and Banach spaces. The purpose of this paper is to provide a method for obtaining a solution to the equilibrium problem in Banach spaces. In fact, we consider a hybrid proximal point algorithm...

*Correspondence: [email protected] African University of Science and Technology, Abuja, Nigeria Abstract Let E be a real normed space with dual space E∗ and let A : E→ 2E be any map. Let J : E→ 2E be the normalized duality map on E. A new class of mappings, J-pseudocontractive maps, is introduced and the notion of J-fixed points is used to prove that T := (J – A) is J-pseudocontractive if an...

We study a class of chainable continua which contains all inverse limit spaces generated by single interval bonding map is piecewise monotone and locally eventually onto. Such are realized as attractors non-hyperbolic surface homeomorphi

In an earlier paper 1] two of us studied generalized transfer operators M associated to maps of intervals of R. In particular the analyticity of a sharp determinant Det # (1?zM) was analyzed on the basis of spectral properties of M and by relating Det # (1 ? zM) to the determinant of 1 + D(z) for a suitable kneading operator D(z). It is a natural idea to try to replace monotone maps of interval...

In an attempt to bootstrap classical homotopy theoretic tools into the world of abstract spacetime, we identify a criterion under which two maps of compact pospaces which are homotopic in the classical sense are also homotopic through monotone maps. As a corollary, we show that a hypercontinuous lattice equipped with its Lawson topology is contractible through monotone maps if its underlying sp...

We study piecewise monotone and piecewise continuous maps f from a rooted oriented tree to itself, with weight functions either piecewise constant or of bounded variation. We deene kneading coordinates for such tree maps. We show that the Milnor-Thurston relation holds between the weighted reduced zeta function and the weighted kneading determinant of f. This generalizes a result known for piec...

We show that if P is a quadratic polynomial with a fixed Cremer point and Julia set J , then for any monotone map φ : J → A from J onto a locally connected continuum A, A is a